I was recently working with a Year 10 Mathematical Methods student, in preparation for the upcoming exams. She couldn’t remember the exact values of the Unit Circle angles, so I showed her a handy method of remembering. She was impressed (aw, shucks!), so I thought I’d share it here!
Label the thumb of your left hand “SINE”, your index finger “30”, your middle finger “45”, your ring finger “60” and your pinky “COS”. Draw a vinculum with the number 2 as the denominator on your palm. Or, draw divided by 2 on your palm – whichever works!
Step 2 requires some imagination. I want you to imagine that there is a magic square root symbol floating in the air above your fingertips. Can you see it?
If you would like to know what the exact value of, say, Sine 30 degrees, fold down the finger with “30” on it. Like this:
The Magic Root symbol goes over the digit left standing on the Sine side of the hand – in this case the thumb. The root of one (or just one), divided by two – the exact value of Sine 30 is one-half!
Can you also see how the Cosine of 30 can be found?
Below I have lowered the “45” digit – the Sine and Cosine of 45 both equal to root two divided by two! It’s magic!
This little memory trick has worked wonders for me over the past few years, particularly with students who have found surds and fractions to be a frightening mix. I have taught this to students in Year 10, who have found it an invaluable tool in their understanding of the Unit Circle.
Here’s a challenge for you or your students. How can we include the exact values for the Tangent into this?